That doesn't mean you should stop running, just that it is a decision with consequences like any other.
The point being once you get into serious mileage like the 30+ miles per week, doing 15-20 mile training runs and racing 1/2 and full marathons its best to view them as personal performance goals vs health goals.
Also, as someone who has run long distance for about 10 years now, take it from me that rest is as important as the miles. Making sure you have rest build into your training plan and after your goal race. This will help you avoid burnout and injuries. Remember, all training really does is takes your body to a stressing point. Its the rest portion that allows your body to respond and adapt to the stress which in turn allows your body to perform at a higher level of performance.
For a very rough wedge, suppose there were some other activity which didn't have all the positive perceptions around running, which created painful and debilitating injuries requiring medical attention as a matter of course, whose participants could all expect to require specialized medical equipment to go about their lives for a period of weeks to months, several times in their careers in that activity. Imagine there were a whole cottage industry of doctors specialized in patching these people back up and sending them on their way to go get injured again, driving up insurance premiums for the rest of us in the process. Imagine that this activity, and this industry, primarily targeted children and adolescents.
We'd go apeshit. There would be immense moral panic.
A cross country runner at my high school was newly on crutches every other week, sometimes for the third time, and no one batted an eye. Orthopedic surgeons make their careers on relationships with the families of athletic teenagers, and no one bats an eye.
Coming from a background where painful, traumatic injuries are not just something that happens to everyone on a regular basis, statements like "I don't see any harm" are insane.
(Yes, I know it is possible to exercise in ways that mitigate this risk, and I do so. Still, if you really think about it, it's kind of crazy how much we tolerate sports injury).
Maybe that coach had some bad ideas.
Also, in my experience, a vast majority of pupils and students who were injured did it during a sport activity and not because of other kinds of accidents.
I see you're new here
The current available evidence found no significant difference in all-cause mortality or CHD mortality, resulting from the dietary fat interventions. [2]
[1] Intake of saturated and trans unsaturated fatty acids and risk of all cause mortality, cardiovascular disease, and type 2 diabetes: systematic review and meta-analysis of observational studies. BMJ. 2015 Aug 11;351:h3978. doi: 10.1136/bmj.h3978. http://www.ncbi.nlm.nih.gov/pubmed/26268692
[2] Evidence from randomised controlled trials does not support current dietary fat guidelines: a systematic review and meta-analysis. Open Heart. 2016 Aug 8;3(2):e000409. doi: 10.1136/openhrt-2016-000409. http://www.ncbi.nlm.nih.gov/pubmed/27547428
http://www.nhs.uk/news/2016/07July/Pages/Study-finds-link-be...
(the linked article talks about these various studies; have a quick read of it)
All that said, though, I agree that the impact of saturated fat on health is hardly clear-cut. As someone else in the comments mentioned, the best advice is probably the oldest: Moderation in all things -- including moderation.